cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A154454 Signature permutation of a Catalan bijection: The inverse of A154453.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 19, 21, 22, 16, 20, 17, 18, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 51, 52, 56, 58, 59, 60, 62, 64, 63, 42, 43, 53, 57, 61, 44, 54, 45, 46, 47, 55, 48, 49, 50, 65, 66, 67, 68, 69, 70, 71
Offset: 0

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Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 000... ray, but not starting swapping until at the left-hand side child of the root, leaving the root itself fixed. Specifically, *A154454 = psi(A154444), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154453. a(n) = A069768(A154452(n)) = A057163(A154450(A057163(n))). Cf. A069770, A154456.
Differs from its inverse A154453 for the first time at n=49, where a(49)=64, while A154454(49)=63. Differs from A089854 for the first time at n=49, where a(49)=64, while A089854(49)=63. Differs from A131173 for the first time at n=26, where a(26)=26, while A131173(26)=27.

A154449 Signature permutation of a Catalan bijection induced by generator "a" of the rightward recursing instance of Basilica group wreath recursion: a = (1,b), b = s(1,a).

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 11, 9, 10, 15, 14, 16, 17, 18, 19, 20, 21, 22, 32, 31, 34, 35, 36, 30, 33, 28, 23, 24, 29, 25, 26, 27, 40, 41, 39, 37, 38, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 91, 92, 90, 87, 88, 97, 96
Offset: 0

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the rightmost tip of the tree along the 111... ray, so that the last vertex whose descendants are swapped, is the right-hand side child of the root and the root itself is fixed. Specifically, *A154449 = psi(A154439), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154450. a(n) = A154455(A069768(n)) = A057163(A154453(A057163(n))). Cf. A154451.

A154443 Permutation of nonnegative integers induced by Basilica group generating wreath recursion: a = (b,1), b = s(a,1), starting from the inactive (fixing) state a.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 10, 11, 8, 9, 12, 13, 14, 15, 21, 20, 22, 23, 16, 17, 18, 19, 24, 25, 26, 27, 28, 29, 30, 31, 42, 43, 40, 41, 44, 45, 46, 47, 32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 85, 84, 86, 87, 80, 81, 82, 83
Offset: 0

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Links

Crossrefs

Inverse: A154444. a(n) = A154441(A153141(n)) = A054429(A154439(A054429(n))). Cf. A072376, A153141-A153142, A154435-A154436, A154439-A154448. Corresponds to A154453 in the group of Catalan bijections.

Extensions

Spelling/notation corrections by Charles R Greathouse IV, Mar 18 2010

A154451 Signature permutation of a Catalan bijection induced by generator "b" of the rightward recursing instance of Basilica group wreath recursion: a = (1,b), b = s(1,a).

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 6, 4, 5, 18, 17, 20, 21, 22, 16, 19, 14, 9, 10, 15, 11, 12, 13, 49, 50, 48, 45, 46, 55, 54, 57, 58, 59, 61, 62, 63, 64, 47, 44, 53, 56, 60, 42, 51, 37, 23, 24, 38, 25, 26, 27, 43, 52, 39, 28, 29, 40, 30, 31, 32, 41, 33, 34, 35, 36, 143, 142, 146, 147, 148
Offset: 0

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the rightmost tip of the tree along the 111... ray, so that the last vertex whose descendants are swapped is the root node of the tree. Specifically, *A154451 = psi(A154441), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154452. a(n) = A154453(A069768(n)) = A057163(A154455(A057163(n))). Cf. A069770, A154449.

A154455 Signature permutation of a Catalan bijection induced by generator "b" of the leftward recursing instance of Basilica group wreath recursion: a = (b,1), b = s(a,1).

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 6, 4, 5, 17, 18, 20, 21, 22, 16, 19, 14, 9, 10, 15, 11, 13, 12, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 44, 47, 53, 56, 60, 42, 51, 37, 23, 24, 38, 25, 26, 27, 43, 52, 39, 28, 29, 41, 33, 35, 36, 40, 30, 34, 31, 32, 129, 130, 132, 133, 134
Offset: 0

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the leftmost tip of the tree along the 000... ray, so that the last vertex whose descendants are swapped is the root node of the tree. Specifically, *A154455 = psi(A154445), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154456. a(n) = A154449(A069767(n)) = A057163(A154451(A057163(n))). Cf. A069770, A154453.
Differs from A082345 for the first time at n=49, where a(49)=26, while A082345(49)=27. Differs from A122327 for the first time at n=26, where a(26)=49, while A122327(26)=50. Differs from A129612 for the first time at n=195, where a(195)=92, while A129612(195)=91.
Showing 1-5 of 5 results.

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